cp's OEIS Frontend

A080371 a(n) is the smallest x such that the quotient d(x+1)/d(x) equals n, where d = A000005.

%I A080371 #35 Jan 27 2021 08:26:40
%S A080371 2,1,11,23,47,59,191,167,179,239,5119,359,20479,2111,719,839,983039,
%T A080371 1259,786431,3023,2879,15359,62914559,3359,22031,266239,6299,6719,
%U A080371 13690208255,5039,22548578303,7559,156671,6881279,25919,10079,1168231104511,5505023,479231,21839
%N A080371 a(n) is the smallest x such that the quotient d(x+1)/d(x) equals n, where d = A000005.
%C A080371 a(37) > 10^12. - _Donovan Johnson_, Sep 02 2013
%C A080371 Conjecture: a(p) = 2^(p-1) * k - 1 for some k > 0 and prime p. - _David A. Corneth_, Jan 26 2021
%H A080371 David A. Corneth, <a href="/A080371/b080371.txt">Table of n, a(n) for n = 1..196</a>
%H A080371 Donovan Johnson, <a href="/A080371/a080371.txt">All 435 terms <= 10^12</a>
%F A080371 a(n) = Min_{x : d[x+1]/d[x] = n}.
%F A080371 a(n) = A086551(n) - 1. - _Hugo Pfoertner_, Jan 26 2021
%e A080371 n = 49: a(49) = 233279 = m, d(m+1) = 98, d(m) = 2, quotient = 49.
%t A080371 t = Table[ 0, {50}]; Do[ s = DivisorSigma[0, n+1] / DivisorSigma[0, n]; If[ s < 51 && t[[s]] == 0, t[[s]] = n], {n, 1, 10^8}]; t
%o A080371 (PARI) {a(n) = my(k=1); while(numdiv(k+1)!=n*numdiv(k), k++); k} \\ _Seiichi Manyama_, Jan 17 2021
%Y A080371 Cf. A000005, A080372.
%K A080371 nonn
%O A080371 1,1
%A A080371 _Labos Elemer_, Feb 24 2003
%E A080371 More terms from _Robert G. Wilson v_, Feb 27 2003
%E A080371 a(29) and a(31) from _Donovan Johnson_, Dec 26 2012
%E A080371 More terms from _David A. Corneth_, Jan 27 2021